Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > Mathboxes > sscoll2 | Unicode version |
Description: Version of ax-sscoll 13982 with two disjoint variable conditions removed and without initial universal quantifiers. (Contributed by BJ, 5-Oct-2019.) |
Ref | Expression |
---|---|
sscoll2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 108 | . . . . . 6 | |
2 | rexeq 2666 | . . . . . . 7 | |
3 | 2 | adantl 275 | . . . . . 6 |
4 | 1, 3 | raleqbidv 2677 | . . . . 5 |
5 | eleq2 2234 | . . . . . . . . . 10 | |
6 | 5 | adantr 274 | . . . . . . . . 9 |
7 | 6 | imbi1d 230 | . . . . . . . 8 |
8 | 7 | ralbidv2 2472 | . . . . . . 7 |
9 | 6 | anbi1d 462 | . . . . . . . . 9 |
10 | 9 | rexbidv2 2473 | . . . . . . . 8 |
11 | 10 | ralbidv 2470 | . . . . . . 7 |
12 | 8, 11 | anbi12d 470 | . . . . . 6 |
13 | 12 | rexbidv 2471 | . . . . 5 |
14 | 4, 13 | imbi12d 233 | . . . 4 |
15 | 14 | albidv 1817 | . . 3 |
16 | 15 | exbidv 1818 | . 2 |
17 | ax-sscoll 13982 | . . . 4 | |
18 | 17 | spi 1529 | . . 3 |
19 | 18 | spi 1529 | . 2 |
20 | 16, 19 | ch2varv 13762 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wex 1485 wral 2448 wrex 2449 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-sscoll 13982 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |